Logic and Set Theory around the World - Sylvain Poirier
Research groups and departments in the foundations of mathematics and computer science (logic, set theory, model theory, theoretical computer science, proof theory, programming languages). Browse the listing by geographic region. See also Poirier's index of organizations, publications, blogs, mailing lists, software, and more.
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Mathematical Logic and Foundations - Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to mathematical deduction. The subject has origins in philosophy, and indeed it is only by nonmathematical argument that one can show the usual rules for inference and deduction (law of excluded middle; cut rule; etc.) are valid. It is also a legacy from philosphy that we can distinguish semantic reasoning ("what is true?") from syntactic reasoning ("what can be shown?"). The first leads to Model Theory, the second, to
Proof Theory. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.
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Set Theory and Foundations (MathPages) - Kevin Brown
About 30 "informal notes" by Kevin Brown on set theory and foundations: what is fuzzy logic, fractal logic, Cantor's diagonal proof, are all triangles isosceles?, on Gauss's mountains, problems with the luminiferous aether, and many more.
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alt.math.undergrad - Math Forum
An unmoderated discussion forum for issues and problems pertaining to college undergraduate mathematics. Read and search archived messages; and register to post to the discussions.
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Aristotle and the Paradoxes of Logic - Gilbert Voeten
At about the same time that set theory began to influence other branches of mathematics, various contradictions, called paradoxes, were discovered. A paradox, however, is only due to a striking violation of at least one of Aristotle's laws of logic. The
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Association for Symbolic Logic
The Association for Symbolic Logic (ASL) is an international organization supporting the presentation, publication, and critical discussion of scholarly work in the field of logic. Its current membership reflects the longstanding important role of logic
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The Battle of The Frog and The Mouse - John Hays
In the 1920s, Albert Einstein heard of a Foundational debate between Formalist
David Hilbert and Intuitionist L.E.J. Brouwer, and asked: "What is this frog and mouse battle between the mathematicians?" This fable presents Brouwer as the frog, Hilbert
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Blacks Academy - Blacks Academy
Extensive database of high school level resources for mathematics, suitable for teachers and independent students. Free with registration required. British-based curricula are served, but could be of great interest to American students, including sophomores.
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Boolify - The Public Learning Media Laboratory
Visualize the process of searching the web by interacting with the abstract logic concept behind queries -- as jigsaw puzzle pieces of keywords and Boolean operators (AND, OR, NOT). Boolify offers a video and several lesson plans in a web search curricula.
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BrainBashers - Kevin N. Stone
A collection of logic, language and math puzzles, in a choice of easy/medium/hard. Rate the puzzles; show their answers. Logic puzzles include Einstein's Puzzle. Play games of strategy, such as "Four in a Row" (also known as "Connect Four") or games based
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Brainers - PedagoNet
More than 60 word problems and puzzles designed to develop logic and problem-solving skills. Submit your answers and suggestions to become part of the Wall of Fame. Site is in English, French, and Spanish.
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Bricks Activity - Suzanne Alejandre
A classroom activity (also called the Masonry Problem; a variation on polyominoes) aligned to the NCTM and California Standards, to be explored through manipulatives (dominoes). Students explore different possibilities of making brick walls with and without
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Bridge to Higher Mathematics - Sam Vandervelde
Textbook for use with the proofs course taught at St. Lawrence University by Vandervelde, an Associate Professor of Mathematics who writes questions for the USA Math Olympiad. Bridge to Higher Mathematics incorporates "concept checks" and "mathematical
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Category Theory Demonstrations - Jocelyn Paine
This is a Web page with buttons that generate examples, with diagrams, of concepts in category theory. These include: initial and terminal objects, products and coproducts, equalisers and coequalisers, pullbacks and pushouts, and limits and colimits.
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